Dual-parameter regularization method in three-dimensional ionospheric reconstruction

Abstract. Ionospheric tomography based on the total electron content (TEC) data along the ray path from Global Navigation Satellite Systems (GNSS) satellites to ground receivers is a typical ill-posed inverse problem. The regularization method is an effective method to solve this problem, which incorporates prior constraints to approximate the real ionospheric variations. When two or more prior constraints are used, the corresponding multiple regularization parameters are introduced in the cost functional. Assuming that the ionospheric spatial variations can be separable in the horizontal and vertical directions, different prior constraints are used in each direction, and the dual-parameter regularization algorithm is established to reconstruct the three-dimensional ionospheric electron density in the present paper. To make the reconstruction results comprehensively reflect the observation information and background (prior) information, it is crucial to determine the optimal regularization parameters. The linear model function method is used to choose these regularization parameters. Both an ideal test and a real test show that this regularization algorithm can effectively improve the background model output.